Use the relationships between angle pairs to find the measure of angle f.

Angle a and angle b are complementary angles. Write an equation to represent the relationship between angle a and angle b.
dºcºbºaºfºeº
Great job!
Angle a and angle f are supplementary angles. Write an equation to represent the relationship between angle a and angle f.
a+b=90
dºcºbºaºfºeº
Good work!
The measure of angle b is 38°. You want to find the measure of angle f. You know the measure of angle b, so let's start by using the first equation to find the measure of angle a. Solve on paper. Then, enter your answer on Zearn.
dºcºb = 38ºaºfºeº
a+b=90
a+f=180

a=

1 answer

To find the measure of angle \( a \), we start with the equation for complementary angles:

\[ a + b = 90^\circ \]

Given that the measure of angle \( b \) is \( 38^\circ \), we can substitute this value into the equation:

\[ a + 38 = 90 \]

Now, to isolate \( a \), we subtract \( 38 \) from both sides:

\[ a = 90 - 38 \] \[ a = 52^\circ \]

Now that we have the measure of angle \( a \) (which is \( 52^\circ \)), we can find the measure of angle \( f \) using the equation for supplementary angles:

\[ a + f = 180^\circ \]

Substituting the value of \( a \):

\[ 52 + f = 180 \]

To isolate \( f \), we subtract \( 52 \) from both sides:

\[ f = 180 - 52 \] \[ f = 128^\circ \]

Thus, the measure of angle \( f \) is \( 128^\circ \).